Methods for characterizing, classifying, and identifying unknowns in samples

ABSTRACT

Disclosed is a method for taking the data generated from an array of responses from a multichannel instrument, and determining the characteristics of a chemical in the sample without the necessity of calibrating or training the instrument with known samples containing the same chemical. The characteristics determined by the method are then used to classify and identify the chemical in the sample. The method can also be used to quantify the concentration of the chemical in the sample.

[0001] The present application is a CIP of U.S. Ser. No. 09/372,641filed Aug. 10, 1999, the disclosure of which is hereby incorporated byreference.

[0002] This invention was made with Government support under ContractDE-ACO676RL01830 awarded by the U.S. Department of Energy. TheGovernment has certain rights in the invention.

FIELD OF THE INVENTION

[0003] The present invention relates generally to a method forcharacterizing, classifying, and identifying unknown chemicals.Specifically, the present invention is a method for taking the datagenerated from an array of responses from a multichannel instrument, anddetermining the characteristics of a chemical in the sample without thenecessity of calibrating or training the instrument with known samplescontaining the same chemical. The characteristics determined by themethod are then used to classify and identify the chemical in thesample. The method can also be used to quantify the concentration of thechemical in the sample.

BACKGROUND OF THE INVENTION

[0004] The characterization and identification of unknown chemical is acommon requirement throughout an enormous variety of scientific inquiry,running across disciplines as diverse as biochemistry and environmentalscience. Unsurprisingly, there exist an equally enormous variety oftechniques for determining the characteristics and identity of achemical in a sample. Liquid and gas chromatography, mass spectroscopy,absorption spectroscopy, emission spectroscopy, and chemical sensors arebut a few of the myriad of techniques scientists have devised in theirefforts to characterize, classify, and identify unknown chemicals insamples.

[0005] Typically, these methods rely on inferences drawn from theinformation that is the output of a particular instrument. For example,methods that identify chemicals through absorption spectroscopy rely onthe absorption of light at certain wavelengths when the samplecontaining the chemical is exposed to a light. By understanding theproperties of a given chemical which give rise to absorption at certainwavelengths, scientists are able to infer some of a sample'scharacteristics and perhaps identity the chemical(s) in the sample forexample, by comparing the absorption spectra of a sample with a libraryof spectra taken from known chemicals. As such, these techniques oftenrely on determining the output signals of an instrument in response tochemicals whose identity and characteristics are known. Additionally,samples of chemicals whose concentrations are unknown may presentproblems for characterizing, classifying, identifying or quantifyingunknowns using these types of instruments. Quantification often relieson rigorous calibration of the instrument in response to known samplesof the chemical to be determined in the unknown samples. To overcomethese and other difficulties, scientists have developed methods whereina sample with an unknown chemical is interrogated with an array ofchannels from a particular instrument, for example, wherein thedifferences in the interactions between the various channels across thearray with different chemicals is known from prior training andcalibration on samples containing the same chemical as the unknownsample.

[0006] For example, a great many studies have described the use ofarrays of chemical sensors to classify, identify, and quantify chemicalsin a sample. Typically in these methods, the sensor array must betrained on samples containing chemicals of known identity andconcentration in order to develop pattern recognition algorithms andcalibration models that are used to classify, identify and quantifychemicals in unknown samples.[B. M. Wise, N. B. Gallagher, and M. W. A.U. S. A. Eigenvector Research, The process chemometrics approach toprocess monitoring and fault detection, J. Process Control, 6 (1996)329-348. K. R. Beebe, R. J. Pell, and M. B. Seasholtz, Chemometrics: APractical Guide, John Wiley and Sons, Inc., New York, 1998.] The onlychemicals that can be classified, identified and quantified by thistechnique are chemicals to which the array has been previously exposedto generate output data that have been incorporated into the developmentof the pattern recognition algorithms and calibration models.

[0007] For example, acoustic wave sensors coated with layers of sorbentmaterials, such as polymers, have been investigated as array detectorsby many groups.[J. W. Grate, S. J. Martin, and R. M. White, AcousticWave Microsensors, Part I, Anal Chem., 65 (1993) 940A-948A. J. W. Grate,S. J. Martin, and R. M. White, Acoustic Wave Microsensors, Part II,Anal. Chem., 65 (1993) 987A-996A. J. W. Grate, and G. C. Frye, “AcousticWave Sensors,” in Sensors Update, VSH, Weinheim, 1996, pp. 37-83.]Polymer-coated acoustic wave sensors are well understood in terms of thesensors' transduction mechanisms and the interactions of analyte specieswith the polymeric sensing layers. A great variety of acoustic wavedevices have been developed and demonstrated for chemical sensingapplications in the gas and liquid phases. These include thickness shearmode (TSM) devices (also known as the quartz crystal microbalance orQCM), surface acoustic wave (SAW) devices, Leaky SAW devices, surfacetransverse wave (STW) devices, Love wave devices, shear-horizontalacoustic plate mode (SH-APM) devices, flexural plate wave (FPW) devices,thin film resonators, and thin rod flexural devices. Acoustic wave vaporsensors respond to any vapor that is sorbed at the sensing surface witha response that is proportional to the amount of vapor sorbed. Thetransduction mechanism of these sensors, which always involves amass-loading contribution and often involves a polymer modulus changecontribution, does not discriminate among sorbed species. Discriminationis dependent largely on the extent to which the applied polymer layerinteracts with and sorbs particular chemical species. In addition, othersensor devices exist that are also sensitive to added mass, such asmicrobar, microbeam, and microcantilever devices.

[0008] The interactions between vapor molecules and polymeric sorbentphases are solubility interactions, which have been modeled andsystematically investigated using linear solvation energy relationships(LSERs).[J. W. Grate, M. H. Abraham, and R. A. McGill, “Sorbent PolymerCoatings for Chemical Sensors and Arrays,” in Handbook of Biosensors:Medicine, Food, and the Environment, CRC Press, Boca Raton, Fla., USA,1996, pp. 593-612.]

[0009] In this approach, vapor solubility properties are characterizedand quantified by solvation parameters related to polarizability,dipolarity, hydrogen bond acidity, hydrogen bond basicity, anddispersion interactions. The solvation parameters are the descriptorsfor vapor characteristics. LSER equations correlate the log of thepartition coefficient of a vapor in a polymer with the vapor solvationparameters using a series of LSER coefficients related to the polymersolubility properties

[0010] LSERs are linear multivariate correlations with solvationparameters that have been applied to many systems, including water/airpartition coefficients, the sorption of vapors by blood and tissue,toxicity of gases and vapors, adsorption on solid sorbents, adsorptionon fullerene, and partitioning into gas-liquid chromatographicstationary phases. In addition, LSERs have been used to correlatevarious sensory measures with solvation parameters, including retentionacross frog olfactory mucosa, respiratory tract irritation, potency,nasal pungency thresholds and odor thresholds. The partitioning ofvapors into sorbent polymers at 298 K has been investigated with LSERs(correlation coefficients were typically 0.99), and these LSER equationshave been used to estimate the responses of polymer-coated surfaceacoustic wave (SAW) vapor sensors. In addition, LSERs have beendeveloped that correlate the responses of polymer-coated SAW devices tovapor solvation parameters. These yield LSER coefficients related topartitioning and detection of vapors with polymer films on SAW devicesurfaces.

[0011] When a polymer-coated acoustic wave vapor sensor is exposed to avapor, the equilibrium distribution of the vapor between the gas phaseand a polymeric sorbent phase on the sensor surface is given by thepartition coefficient, K. This partition coefficient is the ratio of theconcentration of the vapor in the sorbent polymer, C_(S) to theconcentration of the vapor in the gas phase, C_(V) as shown in eq. 1.

K=C _(S) /C _(V)  (1)

[0012] The response of a mass-sensitive acoustic wave sensor toabsorption of a vapor into the polymeric sensing layer is related to thepartition coefficient as shown in eq 2.

Δf _(V) =n Δf _(S) C _(V) K/p  (2)

[0013] The sensor's response to the mass of vapor absorbed, a frequencyshift denoted by Δf_(V), is dependent on the frequency shift due to thedeposition of the film material onto the bare sensor (a measure of theamount of polymer on the sensor surface), Δf_(S), the vaporconcentration, the partition coefficient, and the density of the sorbentphase, p. If the observed response is entirely due to mass-loading, n=1.If a modulus decrease of the polymer due to vapor sorption alsocontributes to the frequency shift, n can be some number greater than 1,with values from 2 to 4 suggested for certain polymers. Whatever thevalue of n, the observed response is proportional to the amount of vaporsorbed as expressed by the partition coefficient.

[0014] The LSER method for understanding and predicting polymer/gaspartition coefficients is based on eq 3, which expresses log K as alinear combination of terms that represent particular interactions.$\begin{matrix}{{\log \quad K} = {c + {rR}_{2} + {s\quad \pi_{2}^{H}} + {a\quad {\sum\alpha_{2}^{H}}} + {b{\sum\beta_{2}^{H}}} + {1\quad \log \quad L^{16}}}} & (3)\end{matrix}$

[0015] In this relationship, R₂, π₂^(H), ∑α₂^(H), ∑β₂^(H),

[0016] and log L¹⁶ are solvation parameters that characterize thesolubility properties of the vapor, where R₂ is a calculated excessmolar refraction parameter that provides a quantitative indication ofpolarizable n and p electrons; π₂^(H)

[0017] measures the ability of a molecule to stabilize a neighboringcharge or dipole; ∑α₂^(H)

[0018] and ∑β₂^(H)

[0019] measure effective hydrogen-bond acidity and basicity,respectively; and log L¹⁶ is the liquid/gas partition coefficient of thesolute on hexadecane at 298 K (determined by gas-liquidchromatography).The log L¹⁶ parameter is a combined measure of exoergicdispersion interactions that increase log L¹⁶ and the endoergic cost ofcreating a cavity in hexadecane leading to a decrease in log L¹⁶.Henceforth, the parameters that describe characteristics of the samplemore generally shall be referred to as “descriptors.” Thus, in the caseof polymer acoustic wave vapor sensors whose responses are modeled withLSERs, the descriptors are the solvation parametersR₂, π₂^(H), ∑α₂^(H), ∑β₂^(H),

[0020] and log L¹⁶. Solvation parameters have been tabulated for some2000 compounds

[0021] The LSER equation for a particular polymer is determined byregressing measured partition coefficients for a diverse set of vaporson that polymer against the solvation parameters of the test vapors. Theregression method yields the coefficients (s, r, a, b, and l) and theconstant (c) in eq 3. These coefficients are related to the propertiesof the sorbent polymer that are complementary to the vapor properties.The necessary partition coefficients for the determination of the LSERare generally obtained by gas chromatographic measurements, but theycould also be determined from the responses of a mass-sensitive acousticwave device with a thin film of the polymer. LSER equations derived fromchromatographic measurements at 298 K have been reported for fourteensorbent polymers suitable for use on acoustic wave devices. The polymerLSER coefficients will be referred to as polymer parameters. Moregenerally, because the polymer is the portion of this multichannelinstrument that directly interacts with the chemical to produce ameasured response, the term “interactive parameters” is inclusive of“polymer parameters”.

[0022] In the past, sorption data for a vapor on multiple gaschromatographic stationary phases has been used in combination with“polymer parameters” describing the stationary phases to obtain valuesfor vapor solubility parameters to be assigned to known vapors. [M. H.Abraham, G. S. Whiting, R. M. Doherty, and W. J. Shuely, Hydrogenbonding. XVI. A new solute solvation parameter, pi2H, from gaschromatographic data, J. Chromatogr., 587 (1991) 213-228. F. Patte, M.Etcheto, and P. Laffort, Solubility Factors for 240 Solutes and 207Stationary Phases in Gas-liquid Chromatography, Anal. Chem., 54 (1982)2239-2247.] The method was not used to characterize or identifyunknowns, nor was a method developed to characterize an unkown atunknown concentration developed.

[0023] Despite these advances, the prevailing paradigm in the use ofmultichannel analytical instruments for classification andidentification of components of samples is that the array must betrained to recognize the component or components of interest. In thisessentially empirical approach, components that were not in the trainingset cannot be classified or identified. Similarly, the paradigm forusing sensor arrays for vapor classification and identification is thatthe array must be trained to recognize the vapor or vapors of interest.In this essentially empirical approach, chemicals that were not in thetraining set cannot be classified or identified. For example, if asensor array instrument is trained and calibrated on samples containingknown chemicals, and then is taken to the field to detect and identifychemicals, it will only be able to identify chemicals that were in thetraining. If it detects a chemical that was not in the training, thatchemical will either be reported as detected but unknown, or it will bemisidentified as being one of the chemicals in the training.Additionally, a general purpose instrument intended to classify oridentify many chemicals would have to be trained on all those chemicals,and would not be able to classify or identify other chemicals. Thusthere exists a need for a method for using the data from multichannelinstruments which is capable of characterizing the properties of unknownchemicals without the necessity of training the multichannel instrumenton those unknown chemicals. Similarly, there exists a need to be able totransform array responses into descriptors of the chemical propertieswhich may then be used to classify and/or identify unknown chemicals.There also exists a need for a method which allows the characterizationand classification of an unknown chemical even if the concentration isunknown, and the quantification of the concentration of an unknownchemical. Finally, there exists a need for a method which allows amultichannel instrument to be trained on a finite set of chemicals andthen be able to apply the instrument to characterization,classification, identification, and/or quantification of additionalchemicals.

OBJECTS

[0024] Accordingly, it is an object of the present invention to providea method for characterizing an unknown sample by obtaining a pluralityof responses from a multichannel instrument, where the plurality ofresponses equal to or greater a plurality of descriptors, the pluralityof responses is related to each of the plurality of descriptors, and theplurality of descriptors is determined from the plurality of responses.

[0025] It is a further object of the present invention to select theplurality of descriptors from the group comprising molecular interactioncharacteristics of the unknown sample, molecular properties of theunknown sample, molecular structural features of the sample, orcombinations thereof.

[0026] It is a further object of the present invention to select theplurality of descriptors which are related to the solubility propertiesof the samples.

[0027] It is a further object of the present invention to select theplurality of descriptors as vapor solvation parameters.

[0028] It is a further object of the present invention to select theplurality of descriptors as parameters in a linear free energyrelationship.

[0029] It is a further object of the present invention to select theplurality of descriptors as parameters in a linear salvation energyrelationship.

[0030] It is a further object of the present invention to select theplurality of descriptors as descriptors in a quantitative structureactivity relationship.

[0031] It is a further object of the present invention to select theplurality of descriptors as parameters in a principle componentsequation.

[0032] It is a further object of the present invention to model theresponse of each channel of a multichannel instrument with an equationincluding a term that is related to the plurality of descriptors.

[0033] It is a further object of the present invention to utilize aresponse of a multichannel instrument which is related to thethermodynamic partitioning of the unknown sample between phases.

[0034] It is a further object of the present invention to utilize aresponse of a multichannel instrument which is related to thepartitioning of the unknown sample between the ambient environment and aplurality of sorbent phases.

[0035] It is a further object of the present invention to utilize amultichannel instrument which utilizes a plurality of gaschromatographic columns.

[0036] It is a further object of the present invention to utilize amultichannel instrument which utilizes a plurality of sensors havingsorbent phases.

[0037] It is a further object of the present invention to utilize amultichannel instrument which utilizes a plurality of sensors havingsorbent phases selected from the group comprising a solid surface, aself assembled monolayer, a molecular multilayer, an amorphous solidphase, a liquid, a membrane and a thin film.

[0038] It is a further object of the present invention to utilize amultichannel instrument which utilizes a stationary sorbent phase. It isa further object of the present invention to utilize a multichannelinstrument which utilizes a sorbent phase as a polymer.

[0039] It is a further object of the present invention to utilize amultichannel instrument which utilizes a plurality of acoustic wavesensors selected from thickness shear mode devices, surface acousticwave devices, Leaky surface acoustic wave devices, surface transversewave devices, Love wave devices, shear-horizontal acoustic plate modedevices, flexural plate wave devices, thin film resonators, and thin rodflexural devices.

[0040] It is a further object of the present invention to utilize amultichannel instrument which utilizes a plurality of acoustic wavesensors coated with polymers and stationary phases.

[0041] It is a further object of the present invention to utilize amultichannel instrument which utilizes a plurality of optical sensors.

[0042] It is a further object of the present invention to utilize amultichannel instrument which utilizes a plurality of chemiresistorsensors.

[0043] It is a further object of the present invention to utilize amultichannel instrument which utilizes a plurality of chemiresitorsensors having a sorbent layer phase and a solid electronic conductor.

[0044] It is a further object of the present invention to utilize amultichannel instrument which utilizes a plurality of electrochemical orfield effect transistor sensors.

[0045] It is a further object of the present invention to utilize amultichannel instrument which utilizes plurality of sensors selectedfrom microbeam, microbar or microcantilever sensors.

[0046] It is a further object of the present invention to characterizean unknown sample, wherein the sample is modeled with a plurality ofdescriptors, by first obtaining a plurality of responses from amultichannel instrument, the plurality of responses equal to or greaterthan the plurality of descriptors, wherein the response from eachchannel of the multichannel instrument includes a term related to theplurality of descriptors and the term related to the plurality ofdescriptors contains coefficients for each descriptor; and determiningthe plurality of descriptors from the plurality of responses.

[0047] It is a further object of the present invention to utilize amultichannel instrument which utilizes coefficients determined frominstrument responses to known compounds.

[0048] It is a further object of the present invention to utilize amultichannel instrument which utilizes coefficients determined frominstrument responses to known compounds to characterize an unknownsample, wherein the sample is modeled with a plurality of descriptors,by obtaining a plurality of responses from a multichannel instrument,the plurality of responses equal to or greater than the plurality ofdescriptors, wherein the response from each channel of the multichannelinstrument includes a term related to the plurality of descriptors,wherein the term related to the plurality of descriptors containscoefficients for each descriptor, defining a matrix P containing thecoefficients, determining the plurality of descriptors from theplurality of responses and the matrix P.

[0049] It is a further object of the present invention to utilize amultichannel instrument which utilizes coefficients determined frominstrument responses to known compounds to characterize an unknownsample, wherein the sample is modeled with a plurality of descriptors byobtaining a plurality of responses from a multichannel instrument, theplurality of responses equal to or greater than the plurality ofdescriptors, wherein the response from each channel of the multichannelinstrument is included in matrix R where R is equal toC10^((VP+1c))M⁻¹N, the descriptors are determined from matrix V, where Vis related to a term of the form {log(C⁻¹RMN⁻¹)−1c}P^(T)(PP^(T))⁻¹; C isa diagonal matrix of the concentrations of the vapors (number of vaporsby number of vapors), M and N are diagonal matrices (number of channelsby number of channels) of particular properties of specific channels ofthe detector, N (number of sensors by number of sensors, or number ofpolymers by number of polymers) is a diagonal matrix of the Δf_(S)values of the sensors, c is a vector of constants, P^(T) is thetranspose of matrix P, P^(T)(PP^(T))⁻¹ is the pseudo-inverse of P, bydefining a matrix P containing the coefficients and determining theplurality of descriptors from the plurality of responses and the matrixP.

[0050] It is a further object of the present invention to utilize amultichannel instrument which utilizes coefficients determined frominstrument responses to known compounds to characterize an unknownsample, wherein the sample is modeled with a plurality of descriptors,by obtaining a plurality of responses from a multichannel instrument,the plurality of responses equal to or greater than the plurality ofdescriptors, wherein the response from each channel of the multichannelinstrument is included in matrix R where R is equal toC10^((VP+1c))D⁻¹F, the descriptors are determined from matrix V, where Vis equal to {log(C⁻¹RDF⁻¹)−1c}P^(T)(PP^(T))⁻¹; where C is a diagonalmatrix of the concentrations of the vapors (number of vapors by numberof vapors), D is a diagonal matrix of the polymer densities (number ofpolymers by number of polymers), F is a diagonal matrix of the Δf_(S)values of the sensors (number of sensors by number of sensors, or numberof polymers by number of polymers), c is a vector of constants, P^(T) isthe transpose of matrix P, P^(T)(PP^(T))⁻¹ is the pseudo-inverse of P,by defining a matrix P containing the coefficients, and determining theplurality of descriptors from the plurality of responses and the matrixP.

[0051] It is a further object of the present invention to utilize amultichannel instrument which utilizes coefficients determined frominstrument responses to known compounds to characterize an unknownsample, wherein the sample is modeled with a plurality of descriptors,by obtaining a plurality of responses from a multichannel instrument,the plurality of responses equal to or greater than the plurality ofdescriptors, wherein the response from each channel of the multichannelinstrument is included in matrix R where R is equal toC10^((VP+1c))D⁻¹F, the descriptors are determined from matrix V, where Vis equal to {log(C⁻¹RDF⁻¹)−1c}P^(T)(PP^(T))⁻¹; where C is a diagonalmatrix of the concentrations of the vapors (number of vapors by numberof vapors), D is a diagonal matrix of the polymer densities (number ofpolymers by number of polymers), F is a diagonal matrix of the Δf_(S)values of the sensors (number of sensors by number of sensors, or numberof polymers by number of polymers), c is a vector of constants, P^(T) isthe transpose of matrix P, P^(T)(PP^(T))⁻¹ is the pseudo-inverse of P,by defining a matrix P containing LSER coefficients determined frommeasurements of thermodynamic partitioning, and determining theplurality of descriptors from the plurality of responses and the matrixP.

[0052] It is a further object of the present invention to utilize amultichannel instrument which utilizes coefficients determined frominstrument responses to known compounds to characterize an unknownsample, wherein the sample is modeled with a plurality of descriptors,by obtaining a plurality of responses from a multichannel instrument,the plurality of responses equal to or greater than the plurality ofdescriptors, wherein the response from each channel of the multichannelinstrument is included in matrix R where R is modeled as a function ofC, S_(V), V′, P′, and S_(P), where, S_(V) contains any sample specificparameters that influence the response independent of the specificinteractions of the sample with each channel, V′ contains said pluralityof sample parameters, P′ contains parameters specific to the propertiesof detector channels, S_(P) contains channel specific sensitivityparameters, and C contains sample concentration information.

[0053] It is a further object of the present invention to utilize amultichannel instrument which utilizes coefficients determined frominstrument responses to known compounds to characterize an unknownsample, wherein the sample is modeled with a plurality of descriptors,by obtaining a plurality of responses from a multichannel instrument,the plurality of responses equal to or greater than the plurality ofdescriptors, wherein the response from each channel of the multichannelinstrument is included in matrix R equal to S_(V)C10^((V′P′))S_(P).

[0054] It is a further object of the present invention to utilizedescriptors determined from matrix V′_(a) equal to {log RS_(P)⁻¹)}P′_(a) ^(T)(P′_(a)P′_(a) ^(T))⁻¹ where V′_(a) and P′_(a) are V′ andP′ augmented to capture S_(V)C.

[0055] It is a further object of the present invention to utilize one ormore of the descriptors determined according to the method of thepresent invention to classify an unknown sample as belonging to a classof chemicals with certain properties.

[0056] It is a further object of the present invention to utilize one ormore of the descriptors determined according to the method of thepresent invention to classify an unknown sample as belonging to a classof chemicals with certain structural features.

[0057] It is a further object of the present invention to utilize one ormore of the descriptors determined according to the method of thepresent invention to compare the descriptors to a table of descriptorsof known chemicals to determine the identity of the unknown sample.

[0058] It is a further object of the present invention to provide amethod for characterizing an unknown sample at an unknown concentration,wherein the sample is modeled with a plurality of descriptors byobtaining a plurality of responses from a multichannel instrument, theplurality of responses equal to or greater than the plurality ofdescriptors, wherein the response from each channel of the multichannelinstrument includes a term related to the plurality of descriptors,wherein the term related to the plurality of descriptors containscoefficients for each descriptor; defining a matrix P_(a) containing thecoefficients and augmented by a vector of ones, determining theplurality of descriptors and concentration from the plurality ofresponses wherein the response is included in matrix R where R is equalto 10^((V) ^(_(a)) ^(P) ^(_(a)) ^(+1c))D⁻¹F; the descriptors andconcentration are determined from matrix Va, where Va is equal to{log(RDF⁻¹)−1c}P_(a) ^(T)(P_(a)P_(a) ^(T))⁻¹, P_(a) is defined as thematrix P augmented by a vector of ones as given in${P_{a} = \begin{bmatrix}P \\1\end{bmatrix}},$

[0059] where P is a matrix containing the coefficients, C is a diagonalmatrix of the concentrations of the vapors (number of vapors by numberof vapors), D is a diagonal matrix of the polymer densities (number ofpolymers by number of polymers), the superscript of −1 denotes theinverse of the matrix, F is a diagonal matrix of the Δf_(S) values ofthe sensors (number of sensors by number of sensors, or number ofpolymers by number of polymers), P_(a) ^(T) is the transpose of P_(a),P_(a) ^(T)(P_(a)P_(a) ^(T))⁻¹ is the pseudoinverse of P_(a).

[0060] It is a further object of the present invention to provide amethod for characterizing an unknown sample at an unknown concentration,wherein matrix Pa contains LSER coefficients determined frommeasurements of thermodynamic partitioning.

[0061] It is a further object of the present invention to provide amethod for characterizing an unknown sample at an unknown concentration,wherein matrix V contains solvation parameters for vapors.

[0062] It is a further object of the present invention to provide amethod for characterizing an unknown sample at an unknown concentration,wherein matrix R contains reponses of acoustic wave vapor sensors withsorbent interactor layers.

[0063] It is a further object of the present invention to provide amethod for characterizing an unknown sample at an unknown concentration,wherein matrix Pa contains LSER coefficients determined frommeasurements of responses of acoustic wave vapor sensors to knownvapors.

[0064] It is a further object of the present invention to provide amethod for characterizing an unknown sample at an unknown concentration,wherein matrix V contains solvation parameters for vapors.

[0065] It is a further object of the present invention to provide amethod for characterizing an unknown sample at an unknown concentration,wherein matrix R contains responses of acoustic wave vapor sensors withsorbent interactor layers.

[0066] It is a further object of the present invention to provide amethod for characterizing an unknown sample at an unknown concentration,utilizing one or more of the descriptors to classify the unknown sampleas belonging to a class of chemicals with certain properties.

[0067] It is a further object of the present invention to provide amethod for characterizing an unknown sample at an unknown concentration,wherein the descriptors are utilized to classify the unknown sample asbelonging to a class of chemicals with certain structural features.

[0068] It is a further object of the present invention to provide amethod for characterizing an unknown sample at an unknown concentration,wherein the descriptors are compared to a table of descriptors of knownchemicals to determine the identity of the unknown sample.

[0069] It is a further object of the present invention to provide amethod for characterizing an unknown sample at an unknown concentration,wherein the sample is modeled with a plurality of descriptors byobtaining a plurality of responses from a multichannel instrument, theplurality of responses equal to or greater than the plurality ofdescriptors, wherein the plurality of responses is related to each ofthe plurality of descriptors; and determining one or more of theplurality of descriptors from the plurality of responses using themethod of inverse least squares, where an individual descriptor, y, ismodeled as a weighted sum of responses according to y=Xb, where X is themeasured response and b is a vector of weights, generally determined byregression b=X⁺y

[0070] It is a further object of the present invention to provide amethod for characterizing an unknown sample at an unknown concentration,wherein the regression is selected from the methods including multiplelinear regression, partial least squares, and principle componentsregression.

[0071] It is a further object of the present invention to provide amethod for characterizing an unknown sample at an unknown concentration,wherein b, the vector of weights for determination of each descriptor,is determined by a regression using responses to known compounds.

[0072] It is a further object of the present invention to provide amethod for characterizing an unknown sample at an unknown concentration,wherein b, the vector of weights for determination of each descriptor,is determined by a regression using responses to known compounds todetermine descriptors from the instrument response to unknowns that werenot among the known compounds.

SUMMARY OF THE INVENTION

[0073] Accordingly, the present invention is a method of characterizinga component of a sample, beginning with the step of analyzing the samplewith a multivariate instrument wherein each channel of the multivariateinstrument gives a response that is related to various descriptors ofthe component.

[0074] A preferred embodiment of the present invention utilizes an arrayof polymer coated acoustic wave sensors as the multichannel instrumentfor data gathering, and is described in detail to provide an example ofthe practice of the present invention. The key aspect of this approachis that polymer-coated sensor responses are related to the solubilityinteractions between the polymer and the vapor, and the vapors'solubility properties are quantified using solvation parameters.Therefore, the response vector from a polymer-coated sensor arrayencodes information about vapor solubility properties, and it istherefore possible, through the method of the present invention, totransform the array data (or response vector) into vapor solvationparameters. These parameters characterize the vapor, and can be used toadditionally classify or possibly identify vapors. In addition, throughthe method of the present invention, the array data can be transformedinto vapor solvation parameters and vapor concentration simultaneously.

[0075] While the invention is described with polymer-coated acousticwave vapor sensors as an example of the present invention, the presentinvention is applicable to, and broadly encompasses, the use of any suchmultichannel instrument as data gathering mechanisms. Thus, the presentinvention should be understood as a method for characterizing acomponent in a samples for which a “spectrum” or pattern has not beendetermined in advance from experimental calibrations using themultichannel instrument, regardless of which multichannel instrument isselected for the gathering of the data. Also, while the polymer-coatedacoustic wave vapor sensors lend themselves to a detection methodrelated to thermodynamic partitioning, the present invention moregenerally relates to the interpretation of data from any multivariatedetector where the response of each channel of the detector can bemodeled by a mathematical relationship (linear, non-linear orcombinations thereof) correlating responses with sample descriptors. Thepresent invention then allows descriptors of chemicals not in thetraining set of the particular instrument to be extracted from theinstrument response. These descriptors characterize the chemical in thesample and can be used to further classify or identify the chemical.

[0076] For example, as will be apparent to one having skill in the art,there exist many other sorbent phases that are not polymers whosesorbent properties can be modeled with linear solvation energyrelationships, and that could be used as sorbent phases on sensors. Inaddition, it is apparent that there exist other relationships and otherdescriptors that can be used to model sorption, partitioning, and otherprocesses relevant to the response of a multivariate analyticalinstrument. It is also apparent that there exist other types of acousticwave sensors, and types of chemical sensors other than acoustic wavesensors whose responses are dependent on the sorption of a compound ontoor into a layer deposited on the surface of the sensor. For example,microbar, microbeam and microcantilever sensors also can detect the massof a chemical sorbed into a layer. Other types of sensors that rely onpartitioning of a compound into a sorbent phase include optical andchemiresistor sensors, and these sensors can be used in arrays withvarious sorbent layers. Another instrument that relies on sorption intomultiple phases is a multicolumn gas chromatograph. Membrane inlet massspectrometers also involve sorption of vapors into a polymeric materialas a part of the process of obtaining an analytical signal. As will beapparent to one having skill in the art, the method of the presentinvention is readily adaptable to all such sensor systems, and thepresent invention should be understood to contemplate and encompass theuse of all such instruments and relationships.

[0077] As used herein, the term “chemical(s)” is inclusive of elementsas identified on the periodic table of the elements, compounds that arecombinations of those elements, and ions that are charged elements orcompounds. As used herein, the term “characteristic(s)” means physicalproperties, chemical properties, molecular interactions, and structuralfeatures of the sample.

[0078] In one approach of the present invention, all the relevantparameters are solved for simultaneously. It is mathematically similarto a classical least squares solution in absorbance spectroscopy, wherethe observed response, R, is used to obtain the concentrations C giventhe analyte pure component responses S. However, in the presentinvention the observed response, R, is used to obtain numerical valuesof the descriptors.

[0079] A second preferred embodiment requires solving for eachdescriptor (vapor parameter in the case of polymer coated acoustic wavesensors) individually. This is the inverse least squares approach, wherean individual descriptor, y, is modeled as a weighted sum of theresponses.

[0080] One advantage of the present invention is that it is notnecessary to know the concentration of the unknown chemical in thesample independently in order to solve for the characteristics of theunknown chemical in the sample. Thus, in the preferred embodiment of thepresent invention utilizing polymer coated acoustic wave sensors, it isnot necessary to know the vapor concentration independently in order tosolve for the vapor solvation parameters. Instead, the solvationparameters and log of the concentration of an unknown vapor can besolved for simultaneously using the responses of an array ofcharacterized sensors.

[0081] The vapor parameters that characterize a chemical in a sample canbe further used to classify the chemical in the sample. For example, avapor could be classified as a hydrogen-bond base on the basis of apostive ∑β₂^(H)

[0082] value. Alternatively, the parameter values could be used toclassify a vapor as belonging to a particular compound class defined bymultiple characteristics, such as a vapor that is both a hydrogen-bondbase and a hydrogen bond acid. Additionally, the parameter values couldbe used to classify a vapor as belonging to a particular compound class,such as aliphatic hydrocarbon, aromatic hydrocarbon, or aliphaticalcohol, to name just a few.

[0083] The vapor parameters can be further used to identify the unknownchemical by comparison with a tabulation of vapor parameters for knownchemicals.

[0084] Thus, the present invention represents a fundamentally differentway to characterize chemical in a sample and to use thatcharacterization to classify and possibly to identify the chemical.Additionally, it offers a fundamentally new way to quantify theconcentration of a chemical from multivariate data. Provided that themultichannel instrument gives responses (multi-variate data) that can bemathematically related to sample descriptors, a chemical can becharacterized even if the multi-channel instrument has never beentrained on that chemical. In addition, the unknown concentration of achemical in a sample can be estimated even if its identity is unknownand no experimental calibrations on that sample have been performed.

[0085] The subject matter of the present invention is particularlypointed out and distinctly claimed in the concluding portion of thisspecification. However, both the organization and method of operation,together with further advantages and objects thereof, may best beunderstood by reference to the following description taken in connectionwith accompanying drawings wherein like reference characters refer tolike elements.

BRIEF DESCRIPTION OF THE DRAWINGS

[0086]FIG. 1. Is a graph of the RMSEP for the 5 vapor LSER parametersand concentration as a function of fraction proportional noise in theresponse for the CLS model in experiments carried out utilizing thepresent invention.

[0087]FIG. 2. Is a graph showing the average number of vapors withinsalvation parameter error bound of two times the standard error as afunction of the noise in the frequency shift response of the array inexperiments carried out utilizing the present invention. The lower trace(solid line) represents the analysis using all 12 polymers, a diverseset. The upper trace (short dashes) represents the results using a 10polymer set lacking strongly hydrogen bond acidic polymers fluoropolyoland SXFA. The middle trace (long dashes) was created using a.diverse setof 10 polymers (PVPR and PVTD left out).

[0088]FIG. 3. Is a graph of the average number of extra matching vaporswithin solvation parameter error bound of two times the standard erroraccording to compound classes, showing in-class and out-of-class errorsin experiments carried out utilizing the present invention. Results areshown for 10% and 20% noise levels in the frequency shift response ofthe array.

[0089]FIG. 4. Is a graph of the RMSEP for the 5 vapor LSER parametersand concentration as a function of fraction proportional noise in theresponse for the ILS models in experiments carried out utilizing thepresent invention.

[0090]FIG. 5. Is an illustration of the method of converting an arrayresponse vector, shown as a bar graph, into descriptors of the detectedvapor, where the descriptors are the solvation parameters from a linearsolvation energy relationship for vapor sorption.

[0091]FIG. 6. Is an illustration of a system for analyzing the responsefrom a multichannel instrument according to various embodiments of theinvention.

DETAILED DESCRIPTION OF THE INVENTION

[0092] Accordingly, these and other objects of the present invention maybe accomplished by first characterizing a sample using a multichannelinstrument to obtain a plurality of responses, and transforming theresponse vector to a set of descriptors related to sample properties.One method of accomplishing this objective is mathematically analogousto classical least squares (CLS) formulations. Matrix R (samples bychannels), containing the responses of the channels of the multichannelinstrument, is first modeled as

R=CS  (4)

[0093] where C is a matrix of concentrations (samples by analytes) and Sis a matrix of pure component spectra (analytes by channels). If S isknown, the concentrations C can be obtained given R.

C=RS ^(T)(SS ^(T))⁻¹  (5)

[0094] Now consider the responses of individual channels of themultichannel instrument, where each response can be described by anequation containing a term which can in turn be estimated by someequation containing descriptors of sample components, coefficients tothose descriptors, and a constant. For example, the response may berelated to an equilibrium constant, K, and log K values may be estimatedby a combination of terms containing descriptors of the chemical,coefficients to those descriptors, and a constant. The LSER in equation3 can be taken as an example of such a relationship. More generally, theterm in the equation for each response is related to the interaction ofa component of the sample with matter or energy involved in themeasurement. That interaction can be related to sample descriptors, andthe instrument channels can be regarded as containing an interactor.

[0095] In matrix algebra, matrix L, containing values related to theinteraction between sample components and measurement channels, can becalculated according to eq 6.

L=VP+1c  (6)

[0096] Matrix V (number of samples by descriptors) contains thedescriptors, and matrix P (coefficients by number of channels) containsthe coefficients or parameters. The descriptors are related to a samplecomponent and the coefficients are related to measurement channelinteractors. The constants of the equations are given by the vector c (1by number of channels), and 1 is a vector of ones (number of samplesby 1) .

[0097] Equation 6 can more generally be regarded as a linearrelationship between a set of descriptors in V used to predict values inL, where the descriptors are weighted by coefficients in P, and therelationship contains a constant.

[0098] The responses of the channels of the multichannel detector can berelated to values in L, for example, log K values, by an equation suchas that in eq 7.

R=C10^((VP+1c)) M ⁻¹ N  (7)

[0099] Matrix R (samples by channels or sensors) contains the responsevalues for particular sample/channel combinations. Matrix C (number ofsamples by number of samples) is a diagonal matrix of the concentrationsof the samples. Matrices M and N (number of channels by number ofchannels) are a diagonal matrices containing constants associated witheach channel of the detector. It is possible that there will beadditional such diagonal matrices also describing other constantsassociated with each channel.. As used herein, the superscript of −1denotes the inverse of the matrix.

[0100] As will be apparent to those having skill in the art, equation 7can be regarded as a form of equation for instrument reponses in R thatare related to chemical concentrations in C, the exponential of a termthat uses the descriptors in a model, and additional diagonal matricescontaining values related to properties of particular sensors orchannels of the multichannel instrument.

[0101] Equation 7 can be rearranged to solve for V using a matrix Rcontaining the observed responses from a multichannel instrument tovarious single samples. A single vector within R represents the patternvector for a sample. The pattern vector can be used to determine thedescriptors of the sample in V provided that the required properties ofthe instrument channels are known. The properties that are required arethe coefficients or parameters in P, the constants in c, and theconstants in M, N, and any additional diagonal matrices containingconstants related to instrument channels. Instrument channels for whichall these values are known shall be defined as ‘characterized’.

[0102] Rearranging, taking the log of both sides, and then subtracting1c from both sides of eq 7, one obtains

log(C ⁻¹ RMN ⁻¹)−1c=VP  (8)

[0103] To solve for the descriptors in V, it is necessary to remove theP matrix from the right side of eq 8. Since P is not a square matrix,and inverses are only defined for square matrices, one cannot simplymultiply by the inverse of P. However, both sides can be multiplied byP^(T)(PP^(T))⁻¹, the pseudo-inverse of P, yielding

{log(C ⁻¹ RMN ⁻¹)−1c}P ^(T)(PP ^(T))⁻¹ =V  (9)

[0104] The superscript T denotes the transpose of a matrix. It isimportant to note that the PP^(T) term represents a square matrix of thesame rank as P. It should be easily invertible provided that the Pmatrix is of full rank, i.e., the set of interactors exhibitsindependent variations in all interactor parameters. The PP^(T) termmust be well conditioned, and the stability of the approach requiresthat a diverse set of interactors is included in the array.

[0105] Eq 9 indicates that the responses of the “characterized” channelsof a multichannel instrument to a test sample at a known concentrationcan be used to determine the descriptors of the test sample. The sampleof unknown identity but known concentration is characterized in terms ofits descriptors. These descriptors can be used to further classify oridentify the sample.

[0106] However, in the characterization, classification, oridentification of an unknown sample, the concentration would not beknown. Therefore, the real question is whether the parameters for anunknown sample can be determined without the concentration, i.e. can onesolve for the parameters in V without C?

[0107] To accomplish this, two new matrices are defined. The matrixV_(a) is the matrix V augmented by the log of the sample concentrations.Thus, this matrix has a column containing log of sample concentrationsin addition to the columns containing sample descriptors. In matixalgebra,

V _(a) =[Vlog(diag(C))]  (10)

[0108] Similarly, a matrix P_(a) is defined as the matrix P augmented bya vector of ones of appropriate dimension (one by number of channels inthe multichannel instrument). Thus, this matrix contains a row of onesat the bottom in addition to the rows of parameters. In matrix algebra,$\begin{matrix}{P_{a} = \begin{bmatrix}P \\1\end{bmatrix}} & (11)\end{matrix}$

[0109] Using these new matrices, eqs 12-14 can be derived following theapproach in eqs 7-9.

R=10^((V) ^(_(a)) ^(P) ^(_(a)) ^(+1c)) M ⁻¹ N  (12)

log(RMN ⁻¹)−1c=V _(a) P _(a)  (13)

{log(RMN ⁻¹)−1c}P _(a) ^(T)(P _(a) P _(a) ^(T))⁻¹ =V _(a)  (14)

[0110] Equation 12 is essentially the same as eq 7, except that the logof the sample concentrations has been placed in the exponential term.This is equivalent to placing the concentration in front of theexponential term as in 7, since multiplying by a constant is the same asadding to a log term. It is assumed in these equations that all thechannels in the instrument give responses that are linear withconcentration within the concentration range being considered. Then thedifference in pattern from one concentration to another is simply acommon multiplicative factor across all channels. Also, in eq 14,P_(a)P_(a) ^(T) must be invertible.

[0111] Equation 12 can be regarded as a form of equation for instrumentresponses in R that are related to the exponential of a term includingthe descriptors and the sample concentration, and additional diagonalmatrices containing values related to properties of particular channelsof the multichannel instrument. Furthermore, the responses of the“characterized” channels of a multichannel instrument to a test sampleat an unknown concentration can be used to determine the descriptors ofthe test sample and the concentration of the test sample.

[0112] According to eq 14 the parameters and log of the concentration ofan unknown sample can be solved for simultaneously using the responsesof characterized channels of a multichannel instrument. The test sampleof unknown identity and unknown concentration is characterized in termsof its descriptors. These descriptors can be used to further classify oridentify the sample. In addition, the concentration of a sample can beestimated even if its identity is unknown and no experimentalcalibrations on that sample have been performed.

[0113] A second approach requires solving for each descriptorindividually. This is the inverse least squares approach, where anindividual descriptor, y, is modeled as a weighted sum of the responses

y=Xb  (15)

[0114] where X is the measured response and b is a vector of weights,generally determined by regression:

b=X ⁺ y  (16)

[0115] where X⁺ is the pseudoinverse of X. This pseudoinverse is defineddifferently depending upon the type of regression to be used. Inmultiple linear regression (MLR, i.e., ordinary least squares)

X ⁺=(X ^(T) X)⁻¹ X ^(T)  (17)

[0116] In systems where the variables in X are expected to collinearother pseudoinverses are used such as those defined by PrincipalComponents Regression (PCR) or Partial Least Squares (PLS) regression.

[0117] In this approach, y would correspond to one of the sampleparameters or concentration and X would be the (log) multichannelresponse. In this system, colinearity is expected any time the number ofsensors in the array is greater than the number of descriptors and MLRwould not be an appropriate technique for developing a model of the formin equation 15. In such cases, it is preferred that the PLS method beused.

[0118] While the general nature and operation of the present inventionhas been shown and described, a more in depth understanding of theinvention may be acquired through a discussion of some preferredembodiments of the present invention. While the examples provided inthese preferred embodiments are illustrative of the nature and operationof the present invention, those skilled in the art will recognize thatthe general principles demonstrated in the preferred embodiments arereadily applicable in a wide variety of multichannel instruments.Accordingly, the following description of the present invention shouldonly be regarded as illustrating the practice of the present invention,and the invention as claimed in the concluding portion of thisspecification should not be limited to the particular multichannelinstrument described in the following preferred embodiments, but rathershould be broadly construed as including other multichannel instruments.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0119] In a preferred embodiment of the present invention,characterization of vapors using sensor array responses to obtain vaporsolvation parameters is formulated in a manner analogous to classicalleast squares (CLS) formulations used in absorbance spectroscopy. As inthe more general summary of the invention, matrix R (samples bychannels), containing the responses of a spectrometer, is modeled as

R=CS  (4)

[0120] where C is a matrix of concentrations (samples by analytes) and Sis a matrix of pure component spectra (analytes by channels). If S isknown, the concentrations C can be obtained given R.

C=RS ^(T)(SS ^(T))⁻¹  (5)

[0121] Responses of individual polymer coated acoustic wave vaporssensors can be estimated as follows. The LSER coefficients and constantsfor polymers can be used in combination with tabulated vapor solvationparamters to calculate a matrix of log K values for hundreds of vaporson those polymers. These log K values can be converted to K values andthen used to estimate sensor responses according to eq 2.

[0122] Calculation of log K values and sensor responses from LSERs canbe reformulated in matrix algebra notation as follows. Matrix L,containing log K values, can be calculated according to eq 6.

L=VP+1c  (6)

[0123] Matrix V (number of vapors by five solvation parameters) containsthe vapor solvation parameters, and matrix P (5 LSER coefficients bynumber of polymers) contains the polymer parameters. The vapor solvationparameters are descriptors of the vapor properties. The constants of theLSER equations are given by the vector c (1 by number of polymers), and1 is a vector of ones (number of vapors by 1) .

[0124] Conversion of the predicted log K values according to eq 6 toestimated sensor responses, assuming mass-loading responses, can then berepresented by eq 7.

R=C10^((VP+1c)) D ⁻¹ F  (7)

[0125] Matrix R (vapors by polymers) contains the estimated responsevalues as frequency shifts for particular vapor/polymer combinations.Equation 7 is similar to eq 2 (n=1), where C (number of vapors by numberof vapors) is a diagonal matrix of the concentrations of the vapors, andF (number of sensors by number of sensors, or in this preferredembodiment, number of polymers by number of polymers) is a diagonalmatrix of the Δf_(S) values of the sensors. Similarly, D (number ofpolymers by number of polymers) is a diagonal matrix of the polymerdensities. Again, as used herein, the superscript of −1 denotes theinverse of the matrix.

[0126] As in the more general description in the Summary of theInvention, this equation shows how the responses of the sensors of thearray can be related to values in L, which are log K values in thisembodiment. A single vector within R represents the pattern vector for avapor. As practiced by this preferred embodiment of the presentinvention, the pattern vector can be used to determine the solvationparameters of the test vapor provided that the required properties ofthe sensors are known.

[0127] The properties of the sorbent films on the sensors that arerequired to practice this preferred embodiment of the present inventionusing polymer-coated acoustic wave vapors sensors are the polymerdensities, the thicknesses of the films on the sensors in terms ofΔf_(S), and the polymer parameters, and the LSER equation constantsrepresented in D, F, P, and c above. Sensors for which these propertiesare known shall be defined as ‘characterized’ sensors.

[0128] Again, rearranging, taking the log of both sides, and thensubtracting 1c from both sides of eq 7, one obtains

log(C ⁻¹ RDF ⁻¹)−1c=VP  (8)

[0129] Again, both sides are then multiplied by P^(T)(PP^(T))⁻¹, thepseudo-inverse of P, yielding

{log(C ⁻¹ RDF ⁻¹)−1c}P ^(T)(PP ^(T))⁻¹ =V  (9)

[0130] The superscript T again denotes the transpose of a matrix. It isimportant to note that in this preferred embodiment of the presentinvention, the PP^(T) term represents a 5 by 5 square matrix of the samerank as P. It should be easily invertible provided that the P matrix isof full rank, i.e., the set of polymers exhibits independent variationsin all five polymer parameters. The PP^(T) term must be wellconditioned, and the stability of the approach requires that a diverseset of polymers representing all the solubility properties of the LSERmodel is included in the array.

[0131] According to eq 9, the responses of an array of characterizedsensors to a vapor of known concentration could be used to determine thesolvation parameters of the test vapor. The test vapor of unknownidentity but known concentration is characterized in terms of itssalvation parameters. These characteristics can be used to furtherclassify or identify the vapor.

[0132] As in the more general description in the Summary of theInvention, two new matrices are again defined. The matrix V_(a) is thematrix V augmented by the log of the vapor concentrations. Thus, thismatrix has a column containing log of vapor concentrations in additionto the five columns containing vapor solvation parameters. In matixalgebra,

V _(a) =[Vlog(diag(C))]  (10)

[0133] Similarly, a matrix P_(a) is defined as the matrix P augmented bya vector of ones of appropriate dimension (one by number of polymers).Thus, this matrix contains a row of ones at the bottom in addition tothe five rows of polymer parameters. In matrix algebra, $\begin{matrix}{P_{a} = \begin{bmatrix}P \\1\end{bmatrix}} & (11)\end{matrix}$

[0134] Using these new matrices, eqs 12-14 can be derived following theapproach in eqs 7-9.

R=10^((V) ^(_(a)) ^(P) ^(_(a)) ^(+1c)) D ⁻¹ F  (12)

log(RDF ⁻¹)−1c=V _(a) P _(a)  (13)

{log(RDF ⁻¹)−1c}P _(a) ^(T)(P _(a) P _(a) ^(T))⁻¹ =V _(a)  (14)

[0135] Equation 12 is again essentially the same as eq 7, except thatthe log of the vapor concentrations has been placed in the exponentialterm. It is again assumed in these equations that all the sensors in thearray give responses that are linear with concentration within theconcentration range being considered. Then the difference in patternfrom one concentration to another is simply a common multiplicativefactor across all sensors. Also, in eq 14, P_(a)P_(a) ^(T) must beinvertible.

[0136] In this preferred embodiment 5 vapor solvation parameters areutilized, and the P_(a)P_(a) ^(T) term will be 6 by 6, which is easilyinvertible provided that the matrix of polymer parameters P is of fullrank (5) and that none of the 5 polymer parameters are constant over allthe polymers. This means the set of polymers in the array must bediverse, as previously noted in connection with eq 9.

[0137] According to eq 14 the solvation parameters and log of theconcentration of an unknown vapor can be solved for simultaneously usingthe responses of an array of characterized sensors. The test vapor ofunknown identity and unknown concentration is characterized in terms ofits solvation parameters. These characteristics can be used to furtherclassify or identify the vapor. In addition, the concentration of avapor can be estimated even if its identity is unknown and noexperimental calibrations on that vapor have been performed.

[0138] A second preferred embodiment requires solving for each vaporparameter individually. This is the inverse least squares approach,where an individual descriptor, y, is modeled as a weighted sum of theresponses

y=Xb  (15)

[0139] where X is the measured response and b is a vector of weights,generally determined by regression:

b=X ⁺ y  (16)

[0140] where X⁺ is the pseudoinverse of X. This pseudoinverse is defineddifferently depending upon the type of regression to be used. Inmultiple linear regression (MLR, i.e., ordinary least squares)

X ⁺=(X ^(T) X)⁻¹ X ^(T)  (17)

[0141] In systems where the variables in X are expected to collinearother pseudoinverses are used such as those defined by PrincipalComponents Regression (PCR) or Partial Least Squares (PLS) regression.

[0142] In this preferred embodiment utilizing polymer coated acousticwave sensors discussed above, y would correspond to one of the vaporsalvation parameters (descriptors) or concentration and X would be the(log) array response. In this system, colinearity is expected any timethe number of sensors in the array is greater than the number of vaporLSER parameters and MLR would not be an appropriate technique fordeveloping a model of the form in equation 15. In such cases, it ispreferred that the PLS method be used.

[0143] In these preferred embodiments, the method described will be mosteffective if the ratio of polymer volume to sensor surface are ismaximized and the surface is minimally adsorptive. This suggests the useof acoustic wave devices such as the QCM or FPW sensor that employthicker polymer films (thickness in absolute terms, not in terms offrequency shift on application). A SAW device tends to use thinnerfilms, and practical film thicknesses decrease with increasing frequencyat the same time the sensitivity to adsorbed mass in increasing.

[0144] Because the acoustic wave device has some sensitivity toadsorption, and may include modulus contributions that are specific toeach polymer, it may be advantageous to obtain the polymer parametersfrom LSERs derived from sensor response data. In this case, acalibration against many vapors of known solvation parameters would berequired to obtain the required polymer parameters. Once this trainingwas complete, the array could still be used to obtain characterizationinformation about vapors that were not in this training set. As noted inthe derivation and the experimental results, the set of polymers shouldbe diverse.

[0145] Although derived for mass-transducing sensors above, thechemometric method for extracting descriptors from multivariateresponses is very general. In a third preferred embodiment descriptorsare extracted through the use of volume-transducing sensors. Sorbentpolymers loaded with conductive particles can be used as chemiresistorvapor sensors where the sensors response, a change in resistance, isrelated to the fractional volume increase of the film on vapor sorption.Carbon-particle loaded polymers for this method of vapor sensing havebeen described and used for array-based sensing. The design of achemiresistor sensor array by varying the properties of the sorbentcomponent of a composite film was proposed by Grate in 1990 inconnection with phthalocyanine/polymer composite Langmuir-Blodgett filmsfor organic vapor sensing. [Grate, J. W.; Klusty, M.; Barger, W. R.;Snow, A. W. Anal. Chem. 1990, 62, 1927-1924.] The phalocyaninenanoparticles served as the current carrying component, and responsecharacteristics were correlated with vapor sorption by the polymercomponent.

[0146] Recently, Severin and Lewis described detailed studies ofcarbon-particle loaded polymer chemiresistors that examined how vaporsoption, volume increases, and sensor resistance changes are related.[Severin, E. J.; Lewis, N. S. Anal. Chem. 2000, 72, 2008-2015.] Theseauthors demonstrated that sensor resistance changes are related to theextent of volume increase regardless of the identity of the vaporproducing the volume increase. Correlation of the response measurementswith vapor densities as liquids supported this mechanism. Therefore,just as acoustic wave sensors represent a very general method of sensingthe mass of vapor sorbed, these carbon/polymer composite chemiresistorsensors represent a very general method of sensing the volume of vaporsorbed. As a result, the signals from an array of these sensors aredirectly related to vapor sorption, and they can be processed accordingto an embodiment of the present invention to obtain analyte descriptors.

[0147] The response function for a volume transducing sensor can beexpressed according to eq 18.

R=φ _(v) S  (18)

[0148] The volume fraction of the vapor in the polymer/vapor solution,φ_(v), times the sensitivity, S, gives the response, R. (It is assumedfor the present analysis that the volume increase due to vapor sorptionis small relative to the initial polymer volume, and the ratio of vaporvolume to polymer volume is nearly the same as the ratio of vapor volumeto the volume of the vapor/polymer solution.) The volume fraction isrelated to the amount of vapor in the polymer, C_(S)=C_(V)K. Thereforethe volume fraction of vapor can be expressed according to eq 19, wherev_(v) is the specific volume of the vapor as a liquid.

φ_(v) =v _(v) C _(V) K  (19)

[0149] Then the response function can be expressed so that the responseis related to vapor specific volume and the concentration, as given ineq 20.

R=v _(v) C _(V) KS  (20)

[0150] The sensitivity, S, in eq 20 has a different value and differentunits than the sensitivity in eq 18 above, but the unchanged notation Sis retained for simplicity.

[0151] It follows that the response function can be expressed in matrixalgebra according to

R=YC10^((VP+1c)) S  (21)

[0152] The matrix Y is a diagonal matrix (number of vapors by number ofvapors) containing the specific volumes of the vapors. Then the solutioncan be expressed as

{log(Y ⁻¹ C ⁻¹ RS ⁻¹)−1c}P ^(T)(PP ^(T))⁻¹ =V  (22)

[0153] This solution, like the initial solution for mass-based sensorsdescribed above, is useful when certain properties of the unknown vapor,in this case the concentration and the specific volume are known togenerate the descriptors in V. In addition, matrix V can be augmented sothat it contains the log of the product of the vapor concentration timesthe vapor specific volume. This augmented matrix will be defined asV_(b). The P matrix is augmented with a vector of ones as before.

R=10^((V) ^(_(b)) ^(P) ^(_(a)) ^(+1c)) S  (23)

{log(RS ⁻¹)−1c}P _(a) ^(T)(P _(a) P _(a) ^(T))⁻¹ =V _(b)  (24a)

{log(rS ⁻¹)−c}P _(a) ^(T)(P _(a) P _(a) ^(T))⁻¹ =v _(b)  (24b)

[0154] Equation 24a expresses the solution for an entire matrix ofresponses, R, while equation 24b expresses the solution where a vectorof descriptors v_(b), is obtained from a single response vector, r.

[0155] This derivation shows how an array of polymer-sorption basedsensors with signals proportional to volume increases can be can be usedto solve for the descriptors of sorbed vapors. One also solves for thevalue of the log of the product of the vapor concentration times thevapor specific volume. While the latter quantity may not ordinarily beof value for classification, if the vapor were identified from the founddescriptors and the specific volume determined, then the concentrationcould be obtained. In any case, the descriptor values can be obtainedand the unknown vapor can be classified. As noted previously, theexistence of this CLS type solution indicates that ILS solutions foreach individual descriptor could be determined by calibration.

[0156] The product of vapor concentration in mass per volume times thevapor specific volume in volume per mass can be regarded as a vaporconcentration in volume per volume units. Although this is a strangeexpression for concentration, regarding this product as a concentrationindicates that the solution in eq 24 for a volume-based sensor array isequivalent to the solution in eq 14 for a mass-based sensor array.

[0157] Vapor specific volume is not highly correlated with the solvationparameters used as descriptors. To verify this, the liquid densities of43 diverse compounds were tabulated with the solvation parameters andexamined for correlations. The correlation matrix is given in Table 1.TABLE 1 Correlation Matrix for Vapor Solvation Parameters and VaporDensity as a Liquid¹ H H H R₂ π₂ Σα₂ Σβ₂ log L¹⁶ d² R₂ 1 0.347 −0.264−0.229 0.576 0.476 H 0 1 0.020 0.507 0.277 0.217 π₂ H 0 0 1 −0.030−0.428 0.124 Σα₂ H 0 0 0 1 0.127 −0.336 Σβ₂ log L¹⁶ 0 0 0 0 1 0.132 d 00 0 0 0 1

[0158] As demonstrated above, the solutions embodied in equations (23)and (24) are generally valid for sensors whose signals are proportionalto volume increases. It is known that the responses of carbonparticle/polymer composite chemiresistor sensors, generally taken as thechange in resistance relative to the initial resistance, areproportional to the relative volume change of the polymeric insulatingphase. For appropriate carbon loadings, the response is linearlyproportional to the vapor concentration and the fractional volumeincrease of the polymer. [Lonergan, M. C.; Severin, E. J.; Doleman, B.J.; Beaber, S. A.; Grubbs, R. H.; Lewis, N. S. Chem. Mater. 1996, 8,2298-2312; Severin, E. J.; Doleman, B. J.; Lewis, N. S. Anal. Chem.2000, 72, 658-668; Severin, E. J.; Lewis, N. S. Anal. Chem. 2000, 72,2008-2015.] Given these characterisitics, this sensor technologyrepresents a volume-transducing method appropriate for a classificationapproach of the present invention.

[0159] In a further embodiment sorption-based sensor arrays whoseindividual sensors respond to both the mass and the volume of the sorbedvapor can be modeled by combining equations 7 and 21, obtaining:

R=C10^((VP+1c)) D ⁻¹ F+YC10^((VP+1c)) S  (25)

[0160] Rather than attempting to derive a closed form solution for vaporparameters V and Y, and concentration C given the response R and polymerparameters P, c, D, F and S, Y is taken as the identify matrix (specificvolumes of the vapors as liquids=1). Under this assumption, thefollowing solution is obtained:

{log(R(D ⁺¹ F+S)⁻¹)−1c}P _(a) ^(T)(P _(a) P _(a) ^(T))⁻¹ =V _(a)  (26a)

{log(r(D ⁻¹ F+S)⁻¹)−c}P _(a) ^(T)(P _(a) P _(a) ^(T))⁻¹ =v _(a)  (26b)

[0161] where V_(a) and P_(a) are defined as before.

[0162] Using this as an initial guess, one can determine V_(a) and Yusing direct fitting of the sensor responses to the model with, forexample, a non-linear least squares optimization procedure. This hasbeen verified on simulated data where the non-linear least squaresoptimization converged to the correct value.

[0163] Polymer-coated acoustic wave vapor sensors responding to both themass of the sorbed vapor and its effect on the polymer modulus representa combined mass and volume transducing sensor technology. [Grate, J. W.Chemical Reviews 2000, 100, 2627-2648; Grate, J. W.; Martin, S. J.;White, R. M. Anal. Chem. 1993, 65, 940A-948A; Grate, J. W.; Martin, S.J.; White, R. M. Anal. Chem. 1993, 65, 987A-996A.] The modulus effectcan be modeled as a volume effect, since modulus changes areproportional to increases in polymer free volume. [Grate, J. W.; Klusty,M.; McGill, R. A.; Abraham, M. H.; Whiting, G.; Andonian-Haftvan, J.Anal. Chem. 1992, 64, 610-624; Martin, S. J.; Frye, G. C.; Senturia, S.D. Anal. Chem. 1994, 66, 2201-2219; Ferry, J. D. Viscoelastic Propertiesof Polymers; 3rd. Ed. ed.; John Wiley and Sons, Inc.: New York, 1980.]Models for SAW vapor sensor response expressed as the sum of mass andvolume terms were reported by Grate in 1992 and 2000. [Grate, J. W.;Klusty, M.; McGill, R. A.; Abraham, M. H.; Whiting, G.;Andonian-Haftvan, J. Anal. Chem. 1992, 64, 610-624; Grate, J. W.;Zellers, E. T. Anal. Chem. 2000, 72, 2861-2868.] These assume thepolymer films on the sensors are acoustically thin. The full model isgiven in eq 27

Δf _(V)=(Δf _(S) C _(V) K/p _(s))+f _(L)(v _(v) C _(V) K)(Δf _(S) A_(SAW)/α)  (27)

[0164] The mass term is the same as the mass term above in equations 2and 7 (where p_(s) is the polymer density). The volume term includes thefractional free volume of the vapor as a liquid, f_(L). The productΔf_(S)A_(SAW)/α gives the frequency change due to a fractional volumeincrease of the polymer film, where α is the coefficient of thermalexpansion of the polymer and A_(SAW) represents the kHz change infrequency due to a 1° C. change in temperature per kHz of coating on thedevice surface. Values for this variable are empirically measured bydetermining the effect of polymer thermal expansion on polymer-coatedSAW device frequency. Assuming that the fractional free volume factor isa constant, the volume term can be reduced to the form in equation 20,giving

Δf _(V)=(Δf _(S) C _(V) K/p _(S))+v _(v) C _(V) KS  (28)

[0165] Thus, this response model fits the form of the matrix model in eq25.

[0166] As can be appreciated by those of skill in the art, theprocedures and methods described herein are not limited to sensorarrays. In a further embodiment, there is provided a classificationmethod for a multivariate detector where the response of each channelcan be modeled with a linear relationship based on a set of sampledescriptors. Unknown samples can then be characterized and classified interms of those descriptors.

[0167] More general response models and solutions can be expressed asfollows.

R=S _(V) C10^((V′P′)) S _(P)  (29)

{log(RS _(P) ⁻¹)}P′ _(a) ^(T)(P′ _(a) P′ _(a) ^(T))⁻¹ V′ _(a)  (30)

[0168] Specific interactions of the analyte with detector channelproperties are modeled in the general linear relationship V′P′, where V′contains analyte descriptors (not necessarily vapor analytes) and P′contains parameters specific to the properties of detector channels. Thematrix S_(V) is a diagonal matrix containing any analyte specificparameters that influence the response independent of the specificinteractions of the analyte with each channel. The matrix Y in eq 21 isan example of a specific S_(V) matrix, containing vapor specific volumesthat influence sensitivity but are not part of VP, whereas in eq 7 S_(V)is the identity matrix. The matrix S_(P) contains channel specificsensitivity parameters, like S in eq 21 or D⁻¹F in eq 7. Augmentation ofV′ and P′ to capture S_(V)C leads to the solution for V′_(a) containingthe analyte descriptors in V′ as well as the log of the product ofanalyte specific sensitivity factor times the analyte concentration.

[0169] As can be appreciated by those of skill in the art, any of theabove methods can be carried out on a system such as a workstationoperatively coupled to a multichannel instrument. The workstation usedwill now be discussed in relation to FIG. 6. In this example embodiment,the various hardware and software components that implement the abovemethods with respect to a response from a multichannel instrument arecombined in workstation 240. Software programs and modules embodying themethods described above are encoded on hard disc 242 for execution byprocessor 244. Workstation 240 may include more than one processor orCPU and more than one type of memory 246, where memory 246 isrepresentative of one or more types. Furthermore, it should beunderstood that while one workstation 240 is illustrated, moreworkstations may be utilized in alternative embodiments. Processor 244may be comprised of one or more components configured as a single unit.Alternatively, when of a multi-component form, processor 244 may haveone or more components located remotely relative to the others. One ormore components of processor 244 may be of the electronic varietydefining digital circuitry, analog circuitry, or both. In oneembodiment, processor 244 is of a conventional, integrated circuitmicroprocessor arrangement, such as one or more PENTIUM II or PENTIUMIII processors supplied by INTEL Corporation of 2200 Mission CollegeBoulevard, Santa Clara, Calif., 95052, USA.

[0170] Memory 246 may include one or more types of solid-stateelectronic memory, magnetic memory, or optical memory, just to name afew. By way of non-limiting example, memory 246 may include solid-stateelectronic Random Access Memory (RAM), Sequentially Accessible Memory(SAM) (such as the First-In, First-Out (FIFO) variety or the Last-InFirst-Out (LIFO) variety), Programmable Read Only Memory (PROM),Electrically Programmable Read Only Memory (EPROM), or ElectricallyErasable Programmable Read Only Memory (EEPROM); an optical disc memory(such as a DVD or CD ROM); a magnetically encoded hard disc, floppydisc, tape, or cartridge media; or a combination of any of these memorytypes. Also, memory 246 may be volatile, nonvolatile, or a hybridcombination of volatile and nonvolatile varieties.

[0171] Detector subsystem 248 provides an interface between workstation240 and multichannel instrument 260. Monitor 250 provides visual outputfrom workstation 250 to an operator. Additional input device(s) 252 andoutput device(s) 254 provide interfaces with other computing and/orhuman entities. Further, detector subsystem 248 and workstation 240 mayinclude additional and/or alternative components as would occur to oneskilled in the art.

EXAMPLE 1

[0172] A series of experiments were undertaken to demonstrate theutility of the present invention as practiced in the preferredembodiments. A matrix of predicted log K values was calculated beginningwith a table of salvation parameters for 280 vapors. The parameters weretaken from published tabulations [M. H. Abraham, J. Andonian-Haftvan, G.Whiting, A. Leo, and R. W. Taft, Hydrogen Bonding. Part 34. The factorsthat influence the solubility of gases and vapours in water at 298 K,and a new method for its determination, J. Chem. Soc., Perkin Trans. 2,(1994) 1777-1791. M. H. Abraham, Scales of hydrogen-bonding: Theirconstruction and application to physicochemical and biochemicalprocesses, Chemical Society Reviews, 22 (1993) 73-83.]

[0173] Vapors included alkanes(24), cycloalkanes (11), alkenes(including dienes and cycloalkenes) (18), terminal linear alkynes (7),fluoroalkanes (2), chloroalkanes (21), bromoalkanes (10), iodoalkanes(7), ethers (8), aldehydes (11), ketones (12), esters (15), nitrites(8), amines (12), nitroalkanes (7), dimethylamides (2), alkanoic acids(6), alcohols (14), fluoroalcohols (3), thiols (7), sulfides (3),organophosphorus compounds (2), aromatic hydrocarbons (11),chlorobenzenes (4), bromo- and iodobenzenes (6), various aromaticcompounds with oxygen-containing functional groups (7), various aromaticcompounds with N-containing functional groups (4), phenols (22), andpyridines (11). The solvation parameter ranges represented by thesevapors were: parameter, range; R₂, -0.64  to  1.453; π₂^(H), 0  to  1.33; ∑α₂^(H), 0  to  0.77; ∑β₂^(H),

[0174] 0 to 1.06; and log L¹⁶, 1.2 to 5.5. LSERs and densities for adiverse set of twelve polymers were taken from previous papers. [J. W.Grate, S. J. Patrash, and M. H. Abraham, Method for estimatingpolymer-coated acoustic wave vapor sensor responses, Anal. Chem., 67(1995) 2162-2169. M. H. Abraham, J. Andonian-Haftvan, C. M. Du, V.Diart, G. Whiting, J. W. Grate, and R. A. McGill, Hydrogen Bonding.XXIX. The characterisation of fourteen sorbent coatings for chemicalmicrosensors using a new solvation equation, J. Chem. Soc., PerkinTrans. 2, (1995) 369-378.] These polymers are listed in Table 2. TABLE 2POLYMERS Abbreviation Description Properties PIB poly(isobutylene)nonpolar aliphatic hydrocarbon material PECH poly(epichlorohydrin)slightly basic ether linkages and slightly dipolar chloromethyl groupsOV25 an OV stationary phase polarizable phenyl groups OV202 an OVstationary phase dipolar nonbasic trifluoropropyl groups PVPR poly(vinylproprionate) moderately basic esters PVTD poly(vinyl tetradecanal)acetal and residual alcohol groups PEM poly(ethylene maleate) dipolarbasic ester linkages SXCN an OV stationary phase dipolar basiccyanopropyl groups PEI poly(ethylenimine) basic amine linkages SXPYR apolysiloxane basic dipolar aminopyridyl groups FPOL fluoropolyol stronghydrogen bond acid SXFA a polysiloxane strong hydrogen bond acid

[0175] The matrix of log K values was converted to a matrix of estimatedsensor responses, assuming mass-loading responses, 250 kHz of materialon each sensor, and a concentration of 5000 mg/m³ for each vapor. Thisproduced a matrix of estimated responses, R, for use in modelingstudies.

[0176] For some purposes, this matrix was divided into a training setwith 195 vapors and a prediction set containing 85 vapors. Vapors fromeach of the various compound classes were distributed proportionatelybetween the training and prediction sets. In addition each vapor waslabeled with a compound class chosen from the list above.

[0177] After setting up the original matrices for V, P, L, and R in anExcel spreadsheet, all further calculations were performed in MATLABVersion 5.2 (The MathWorks, Natick Mass.) with PLS_Toolbox 2.0(Eigenvector Research, Manson, Wash.).

[0178] A matrix R (12 by 280) containing vapor sensor responses Δf_(V)was calculated as described above, where V (5 by 280) containedsolvation parameters for 280 diverse vapors, P (12 by 5) containedpolymer parameters for 12 diverse polymers, and vector c (1 by 12)contained the constants for those polymers. This matrix was used as thebasis for modeling studies to investigate approaches for determiningvapor parameters from sensor array responses. Two subsets of the 12polymer set were also examined in some experiments. Removal of FPOL andSXFA from the 12 polymer set yielded a 10 polymer set lacking a stronghydrogen bond acid polymer. Thus, this represents a less diverse polymerset. Removal of PVPR and PVTD from the 12 polymer set yielded a 10polymer set that preserved chemical diversity in the array.

[0179] Initial calculations were carried out with all vapors at 5000mg/m³ concentration. Given characterized sensors (i.e., D, F, P, and cknown), the vapor parameters, V, can be calculated from R to machineaccuracy. This is simply a rearrangement of the original calculations toobtain R. Then matrix R was modified so that the vapors were at randomconcentrations between 0 and 5000 mg/m . Given characterized sensors, itwas verified that V_(a) could be calculated from R, obtaining the vaporparameters and the vapor concentrations correctly to machine accuracy.Plots of predicted parameters and concentrations against the actualparameters and concentrations are perfectly linear with slopes of one.

[0180] These calculations began with essentially perfect noiseless data.The effect of measurement noise on the determination of vapor parametersand concentration was investigated by adding noise to the sensorresponses in R. The added measurement noise was proportional to theresponse and was normally distributed. The noise was added independentlyacross the polymers.

[0181] Vapor parameters and concentrations were calculated by solvingfor V_(a) and the errors in these results were determined as a functionof the added measurement noise. The root-mean-square errors ofprediction (RMSEP) for each of the parameters and the concentration areplotted versus fraction noise in the data (e.g. 0.1 indicates that thestandard deviation of the noise was 10% of the sensor signal) in FIG. 1.Each line on the plot corresponds to a different set of polymers. Thesolid line includes the 12 polymers in Table 1. With the exception ofconcentration, the errors grow approximately linearly with noise, aswould be expected. Concentration errors grow approximately exponentiallywith noise. This is a result of the fact that the log of theconcentration is predicted, and it must be transformed. The results fora set of ten diverse polymers are similar to those for the twelvepolymer set, but ten polymer arrray lacking hydrogen-bond acid polymersgives poorer results, especially for the ∑β₂^(H)

[0182] parameter (as might be expected).

[0183] The errors in the original solvation parameter scales can betaken as about 0.03 units for the π₂^(H), ∑α₂^(H),

[0184] and ∑β₂^(H)

[0185] parameters. The error for the log L¹⁶ parameter can be taken as0.1 units or less. These parameters are all related to free energies andwere determined from experimental data on partitioning or complexationequilibria. The R₂ parameters is different, since it is calculated frommolar refraction values for liquids, and extended by a groupcontribution scheme. The parameter errors in FIG. 1 for π₂^(H), ∑α₂^(H),

[0186] and ∑β₂^(H)

[0187] are approximately 0.06, 0.02, and 0.03, respectively, for 20%noise in the sensor responses. This is comparable to the error in theoriginal parameters. The log L¹⁶ error at 20% sensor noise is somewhatlarger at 0.3-0.4 log units.

[0188] Once sensor responses in R have been used to solve for V_(a), thefound solvation parameters can be matched to tabulated solvationparameters for known vapors. The effect of measurement noise on thismatching process for vapor identification was examined. Given theprediction error information just described, it is reasonable toconstruct error bounds of two times the RMSEP around each of the vaporparameters for each vapor in V_(a). This is equivalent to a two standarddeviation bound around the predictions. For each vapor, it is possibleto determine how many other vapors in V_(a) fit within this bound. Theoptimal answer is one, where the only vapor that fits within the errorbound is the correct one. As the noise increases and the error boundsincrease, more vapors will fit. The results of this analysis are shownin the lowest trace in FIG. 2, plotting the average number of matchesfor each vapor as a function of the added measurement noise. Here we areconsidering the lower (solid) line on the plot for all 12 polymers. Fornoise levels up to about 10%, typically two or fewer vapors are withinthe error bound, suggesting the ability to identify the correct vaporwill be pretty good up to this noise level. Above this, the number ofvapors within the error bounds tends to grow more rapidly. Nevertheless,even at 20% noise, the number of vapors fitting the solvation parameterswithin error bounds is still limited (ca. 5 or 6). It is worth notingthat this is a conservative evaluation of identification “precision”,since independently derived limits define a larger space than a groupdetermination of the error bounds.

[0189] Vapors within some compound classes tend to have larger numbersof vapors fitting within the error bounds for each vapor than those inother compound classes. For example, there is an average of fifteenvapors, all alkanes, fitting within the error bounds for each alkane atthe 20% noise level. This result is due to the fact that alkanes aredistinguished from one another only by their log L¹⁶ values (i.e,, theyare very similar to one another), the data set contains many alkanes,and many isomers are included. For all other vapor classes the resultsare much better, and the results averaged over all vapors, shown in FIG.2, are skewed to higher values by the poorer results for alkanes. Theplots in FIG. 3 show the average number of vapors fitting within theerror bounds with the correct vapor for each compound class, based onmodeling with all 12 polymers. Henceforth, a compound fitting within theerror bounds for another compound shall be defined as an error. In-classerrors and out-of-class errors are indicated. The results are quite goodat 10% noise and a diverse set of polymers. Except for ethers andketones, most errors are within class. At 20% noise, out-of-class errorsincrease somewhat, especially for ethers, ketones, and aldehydes, allvapors with basic oxygen containing functional groups.

[0190] Because the derivation for this analysis approach indicates thata diverse set of polymers is required, the accuracy of vaporidentification was also examined using a less diverse polymer set. Thetwo hydrogen bond acidic polymers were removed and the results with this10 polymer set were determined, as shown in FIG. 2. Because thesehydrogen bond acidic polymers are not commercially available, this setrepresents the type of less diverse array that will most likely occur.As seen in the graph, vapor classification is not too bad at measurementnoise of 5% or less, but it becomes significantly degraded relative to adiverse array at measurement noise above 10%. To demonstrate that thiseffect is related to diversity rather than polymer number, the sameanalysis was done with a ten sensor array that included the hydrogenbond acidic polymers. This array gives results similar to those of thediverse 12 sensor array (see FIG. 2). The array lacking hydrogen-bondacids yielded more out-of-class errors than the diverse arrays, as foundby examining plots (not shown) similar to those in FIG. 3. At 10% noise,overall results are not bad, but out-of-class errors are notable foresters, ethers, ketones, and aldehydes. At 20% noise, there are largenumbers of out-of-class errors in most compound classes.

[0191] The reason for the effect of polymer diversity on the predictionerror is suggested by the form of eq 12. Note the (P_(a)P_(a) ^(T))⁻¹ inthe equation. If the matrix P_(a)P_(a) ^(T) is ill-conditioned, theproblem will be subject to considerable numerical instability. Smallchanges in the response due to noise will result in large changes in thepredictions, an undesirable effect. The amount of ill-conditioningpresent can be assessed by calculating the condition number of thematrix. The condition number is the ratio of the largest to smallestsingular value of the matrix. When all 12 polymers are considered, thecondition of P_(a)P_(a) ^(T) is 5947. When the hydrogen bond acidpolymers are removed, the condition number jumps to 9562. This increasein the condition number is, in part, responsible for the increase inprediction errors. The condition number of the P_(a)P_(a) ^(T) matrixwas calculated when leaving out PVPR and PVTD was 5998. Thus, leavingout these polymers had little effect on the condition of the matrix.

[0192] Overall, these results demonstrate the concept that a sensorarray consisting of characterized sensors is able to characterize anunknown vapor in terms of its solvation parameters and match it to alimited number of vapor candidates. The technique can also provide anestimate of the unknown concentration. The concentration estimation,however, is much more sensitive to the measurement noise. The derivationfor this approach assumes that patterns are constant regardless of vaporconcentration, i.e., sensor calibration curves are linear. The tolerancefor noise in solving for vapor parameters and matching to known vaporssuggests that the method may also tolerate moderate nonlinearity insensor calibration curves.

EXAMPLE 2

[0193] Modeling was also carried out using ILS methods to determinemodels for each individual vapor parameter from sensor responses asgiven in eq 15 for the vapors in Example 1. In this approach, the sensorresponse data can be empirically used without knowing the polymerparameters. In other words, one need not have characterized sensors asdescribed above. The matrix of sensor responses to particular vapors inV was divided into training and prediction sets. Models were developedusing PLS with six latent variables, training on R and C to get V.

[0194] PLS models developed for each vapor solvation parameters with thesensor responses in the training set were able to predict the parametersfor the vapors in the prediction set to machine accuracy. However, thistest was based on perfect data. The effect of measurement noise wasinvestigated by adding noise to both the training set and the predictionset. PLS models were developed using the training set data with noiseadded. Then the ability to predict the vapor parameters of the vapors inthe prediction set using the “noise-added” response data was tested.

[0195] The results are shown in FIG. 4. These results are very similarto those for the CLS models shown in FIG. 2. In fact, the ILS modelsperform modestly better than the CLS models. Thus, it appears reasonablethat one could train on sensor responses to develop models to predictvapor solvation parameters even if the polymer parameters are not known.These models could then be used to classify unknowns that were not inthe training.

We claim:
 1. A method for characterizing an unknown sample, wherein saidsample is modeled with a plurality of descriptors, comprising the stepsof: a. obtaining a plurality of responses from a multichannelinstrument, said plurality of responses equal to or greater than saidplurality of descriptors, wherein said plurality of responses is relatedto each of said plurality of descriptors; and b. determining saidplurality of descriptors from said plurality of responses.
 2. The methodof claim 1 wherein said plurality of descriptors are selected from thegroup comprising molecular interaction characteristics of said unknownsample, molecular properties of said unknown sample, molecularstructural features of said sample, and combinations thereof.
 3. Themethod of claim 1 wherein said plurality of descriptors are related to aplurality of solubility properties of said samples.
 4. The method ofclaim 1 wherein said plurality of descriptors are vapor solvationparameters.
 5. The method of claim 1 wherein said plurality ofdescriptors are parameters in a linear free energy relationship.
 6. Themethod of claim 1 wherein said plurality of descriptors are parametersin a linear solvation energy relationship.
 7. The method of claim 1wherein said plurality of descriptors are descriptors in a quantitativestructure activity relationship.
 8. The method of claim 1 wherein saidplurality of descriptors are parameters in a principle componentsequation.
 9. The method of claim 1 wherein the response of each channelof said multichannel instrument can be modeled by an equation includinga term that is related to said plurality of descriptors.
 10. The methodof claim 1 wherein the plurality of responses of said multichannelinstrument are related to the thermodynamic partitioning of said unknownsample between phases.
 11. The method of claim 1 wherein the pluralityof responses of said multichannel instrument are related to thepartitioning of said unknown sample between the ambient environment anda plurality of sorbent phases.
 12. The method of claim 1 wherein saidmultichannel instrument utilizes a plurality of gas chromatographiccolumns.
 13. The method of claim 1 wherein said multichannel instrumentutilizes a plurality of sensors having sorbent phases.
 14. The method ofclaim 13 wherein the sorbent phase is selected from the group comprisinga solid surface, a self assembled monolayer, a molecular multilayer, anamorphous solid phase, a liquid, a membrane and a thin film.
 15. Themethod of claim 13 wherein the sorbent phase is a stationary sorbentphase.
 16. The method of claim 13 wherein the sorbent phase is apolymer.
 17. The method of claim 1 wherein said multichannel instrumentutilizes a plurality of acoustic wave sensors selected from the groupcomprising thickness shear mode devices, surface acoustic wave devices,Leaky surface acoustic wave devices, surface transverse wave devices,Love wave devices, shear-horizontal acoustic plate mode devices,flexural plate wave devices, thin film resonators, and thin rod flexuraldevices.
 18. The method of claim 1 wherein said multichannel instrumentutilizes a plurality of acoustic wave sensors coated with polymers andstationary phases.
 19. The method of claim 1 wherein said multichannelinstrument utilizes a plurality of optical sensors.
 20. The method ofclaim 1 wherein said multichannel instrument utilizes a plurality ofchemiresistor sensors.
 21. The method of claim 1 wherein saidmultichannel instrument utilizes a plurality of chemiresitor sensorshaving a sorbent layer phase and a solid electronic conductor.
 22. Themethod of claim 1 wherein said multichannel instrument utilizes aplurality of sensors selected from the group comprising electrochemicaland field effect transistor sensors.
 23. The method of claim 1 whereinsaid multichannel instrument utilizes a plurality of sensors selectedfrom the group comprising microbeam, microbar and microcantileversensors.
 24. A method for characterizing an unknown sample, wherein saidsample is modeled with a plurality of descriptors, comprising the stepsof: a. obtaining a plurality of responses from a multichannelinstrument, said plurality of responses equal to or greater than saidplurality of descriptors, wherein the response from each channel of saidmultichannel instrument includes a term related to said plurality ofdescriptors, wherein said term related to said plurality of descriptorscontains coefficients for each descriptor; and b. determining saidplurality of descriptors from said plurality of responses.
 25. Themethod of claim 24 wherein said coefficients are coefficients in alinear free energy relationship.
 26. The method of claim 24 wherein saidcoefficients are coefficients in a linear solvation energy relationship.27. The method of claim 24 wherein said coefficients are coefficients ina quantitative structure activity relationship.
 28. The method of claim24 wherein said coefficients are coefficients in a principle componentsequation.
 29. The method of claim 24 wherein said coefficients arecoefficients in a linear free energy relationship related to sorbentphase properties.
 30. The method of claim 24 wherein said coefficientsare coefficients in a linear free energy relationship based onthermodynamic partition coefficients.
 31. The method of claim 24 whereinsaid coefficients are determined from instrument responses to knowncompounds.
 32. A method for characterizing an unknown sample, whereinsaid sample is modeled with a plurality of descriptors, comprising thesteps of: a. obtaining a plurality of responses from a multichannelinstrument, said plurality of responses equal to or greater than saidplurality of descriptors, wherein the response from each channel of saidmultichannel instrument includes a term related to said plurality ofdescriptors, wherein said term related to said plurality of descriptorscontains coefficients for each descriptor; b. defining a matrix Pcontaining said coefficients; c. determining said plurality ofdescriptors from said plurality of responses and said matrix P.
 33. Themethod of claim 32 wherein a. the response from said multichannelinstrument is included in matrix R where R is equal to CZ^((VP+1c))M⁻¹Nb. said descriptors are determined from matrix V, where V is related toa term of the form {logz(C⁻¹RMN⁻¹)−1c}P^(T)(PP^(T))⁻¹; c. C is adiagonal matrix of the concentrations of the vapors d. M and N arediagonal matrices of particular properties of specific channels of thedetector, e. the superscript of −1 denotes the inverse of the matrix, f.N is a diagonal matrix of the Δf_(S) values of the sensors, g. c is avector of constants, h. P^(T) is the transpose of matrix P, i.P^(T)(PP^(T))⁻¹ is the pseudo-inverse of P, j. Z is a scalar.
 34. Themethod of claim 32 wherein a. the response is matrix R where R is equalto CZ^((VP+1c))D⁻¹F; b. said descriptors are determined from matrix V,where V is equal to {logx(C⁻¹RDF⁻¹)−1c}P^(T)(PP^(T))⁻¹; c. C is adiagonal matrix of the concentrations of the vapors d. D is a diagonalmatrix of the polymer densities, e. the superscript of −1 denotes theinverse of the matrix, f. F is a diagonal matrix of the Δf_(S) values ofthe sensors, g. c is a vector of constants, h. P^(T) is the transpose ofmatrix P, i. P^(T)(PP^(T))⁻¹ is the pseudo-inverse of P, and j. Z is ascalar.
 35. The method of claim 32 wherein matrix P contains LSERcoefficients determined from measurements of thermodynamic partitioning.36. The method of claim 32 wherein matrix V contains solvationparameters for vapors.
 37. The method of claim 32 wherein matrix Rcontains responses of acoustic wave vapor sensors with sorbentinteractor layers. a. The method of claim 32 wherein matrix P containsLSER coefficients determined from measurements of responses of acousticwave vapor sensors to known vapors.
 38. The method of claim 32 furthercomprising the step of utilizing one or more of said descriptors toclassify said unknown sample as belonging to a class of chemicals withcertain properties.
 39. The method of claim 32 further comprising thestep of utilizing one or more of said descriptors to classify saidunknown sample as belonging to a class of chemicals with certainstructural features.
 40. The method of claim 32 further comprising thestep of comparing said descriptors to a table of descriptors of knownchemicals to determine the identity of said unknown sample.
 41. A methodfor characterizing an unknown sample at an unknown concentration,wherein said sample is modeled with a plurality of descriptors,comprising the steps of: a. obtaining a plurality of responses from amultichannel instrument, said plurality of responses equal to or greaterthan said plurality of descriptors, wherein the response from eachchannel of said multichannel instrument includes a term related to saidplurality of descriptors, wherein said term related to said plurality ofdescriptors contains coefficients for each descriptor; b. defining amatrix P_(a) containing said coefficients and augmented by a vector ofones, c. determining said plurality of descriptors and concentrationwhere from said plurality of responses d. wherein the response is matrixR where R is equal to Z^((V) ^(_(a)) ^(P) ^(_(a)) ^(+1c))D⁻¹F; e. saiddescriptors and concentration are determined from matrix Va, where Va isequal to {logz(RDF⁻¹)−1c}P_(a) ^(T)(P_(a)P_(a) ^(T))⁻¹ f. P_(a) isdefined as the matrix P augmented by a vector of ones as given in${P_{a} = \begin{bmatrix}P \\1\end{bmatrix}},$

where P is a matrix containing said coefficients g. C is a diagonalmatrix of the concentrations of the vapors h. D is a diagonal matrix ofthe polymer densities, i. the superscript of −1 denotes the inverse ofthe matrix j. F is a diagonal matrix of the Δf_(S) values of the sensorsk. P_(a) ^(T) is the transpose of P_(a) l. P_(a) ^(T)(P_(a)P_(a) ^(T))⁻¹is the pseudoinverse of P_(a) m. Z is a scalar.
 42. The method of claim41 wherein matrix P_(a) contains LSER coefficients determined frommeasurements of thermodynamic partitioning.
 43. The method of claim 41wherein matrix V_(a) contains solvation parameters for vapors.
 44. Themethod of claim 41 wherein matrix R contains responses of acoustic wavevapor sensors with sorbent interactor layers.
 45. The method of claim 41wherein matrix P_(a) contains LSER coefficients determined frommeasurements of responses of acoustic wave vapor sensors to knownvapors.
 46. The method of claim 41 further comprising the step ofutilizing one or more of said descriptors to classify said unknownsample as belonging to a class of chemicals with certain properties. 47.The method of claim 41 further comprising the step of utilizing one ormore of said descriptors to classify said unknown sample as belonging toa class of chemicals with certain structural features.
 48. The method ofclaim 41 further comprising the step of comparing said descriptors to atable of descriptors of known chemicals to determine the identity ofsaid unknown sample.
 49. A method for characterizing an unknown sample,wherein said sample is modeled with a plurality of descriptors,comprising the steps of: a. obtaining a plurality of responses from amultichannel instrument, said plurality of responses equal to or greaterthan said plurality of descriptors wherein said plurality of responsesis related to each of said plurality of descriptors; and b. determiningone or more of said plurality of descriptors from said plurality ofresponses using the method of inverse least squares to perform aregression, where an individual descriptor, y, is modeled as a weightedsum of responses according to y=Xb , where X is the measured responseand b is a vector of weights, generally determined by regression b=X⁺y.50. The method of claim 49 wherein wherein the method of regression isselected from the methods including multiple linear regression, partialleast squares, and principle components regression.
 51. The method ofclaim 41 wherein b, the vector of weights for determination of eachdescriptor, is determined by a regression using responses to knowncompounds.
 52. The method of claim 51 wherein b is used to determinedescriptors from the instrument response to unknowns that were not amongsaid known compounds.
 53. A method of characterizing an unknown samplecomprising: obtaining a plurality of responses from a multi channelinstrument, modeling each of said plurality of responses as a functionof a plurality of descriptors, and determining said plurality ofdescriptors from said plurality of responses, wherein said plurality ofresponses is equal to or greater than said plurality of descriptors and,wherein said sample is modeled with said plurality of descriptors. 54.The method of claim 53 wherein: said responses are modeled as a functionof C, S_(V), V′, P′, and S_(P) where, S_(V) contains any sample specificparameters that influence the response independent of the specificinteractions of the sample with each channel V′ contains said pluralityof descriptors, P′ contains parameters specific to the properties ofdetector channels, S_(P) contains channel specific sensitivityparameters, and C contains sample concentration information.
 55. Themethod of claim 54 wherein: said responses are included in matrix Requal to S_(V)CZ^((V′P′))S_(P), where Z is a scalar.
 56. The method ofclaim 55 wherein: said plurality of sample parameters are determinedfrom V′_(a) equal to {logz(RS_(p) ⁻¹)}P′_(a)(P′_(a)P′_(a) ^(T))⁻¹ where;V′_(a) is V′ augmented to contain the log z of the products of thesample specific sensitivity factors and the concentration, and P′_(a) isP′ augmented with a vector of ones, The superscripts of ⁻¹ and ^(T)denote the inverse and transpose of the matrix respectively.
 57. Themethod of claim 56 wherein S_(V) and C are diagonal matrices.
 58. Themethod of claim 57 wherein the sample is a vapor.
 59. The method ofclaim 54 wherein said multi channel instrument includes a plurality ofdiverse sensors that output a signal that depends on the amount of saidsample that interacts with said sensor.
 60. The method of claim 59wherein said amount is selected from the group consisting of mass,volume, and mass plus volume.
 61. The method of claim 60 wherein theamount is a volume and S_(V) is a diagonal matrix with sample specificvolumes.
 62. The method of claim 60 wherein the amount is a mass andS_(V) is the identity matrix.